A mixture of ideal gases consists of 3 kg of nitrogen and 5 kg of carbon dioxide at a pressure of 300 kPa and temperature of $20^{\circ} \mathrm{C}$. Find (i) the mole fraction of each constituent, (ii) the equivalent molecular weight of mixture, (iii) the equivalent gas constant of the mixture, (iv) the partial pressures and the partial volumes, (v) the volume and density of the mixture, and (vi) the $\mathrm{c}_{\mathrm{p}}$ and $\mathrm{c}_{\mathrm{v}}$ of the mixture. If the mixture is heated at constant volume to $40^{\circ} \mathrm{C}$, find the changes in internal energy, enthalpy and entropy of the mixture. Find the changes internal energy, enthalpy and entropy of the mixture if the heating is done at constant pressure. Take $\gamma$ for $\mathrm{CO}_{2}$ and $\mathrm{N}_{2}$ to be 1.286 and 1.4 respectively.
Explanation
To solve this problem, we need to use the formulas for mole fraction, equivalent molecular weight, equivalent gas constant, partial pressures, partial volumes, volume and density of the mixture, and specific heat capacities at constant pressure and constant volume. We also need to use the formulas for change in internal energy, enthalpy and entropy of the mixture when heated at constant volume and constant pressure.
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